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Title: Semi-global approach for propagation of the time-dependent Schrödinger equation for time-dependent and nonlinear problems

Abstract

A detailed exposition of highly efficient and accurate method for the propagation of the time-dependent Schrödinger equation is presented. The method is readily generalized to solve an arbitrary set of ODE's. The propagation is based on a global approach, in which large time-intervals are treated as a whole, replacing the local considerations of the common propagators. The new method is suitable for various classes of problems, including problems with a time-dependent Hamiltonian, nonlinear problems, non-Hermitian problems and problems with an inhomogeneous source term. In this paper, a thorough presentation of the basic principles of the propagator is given. We give also a special emphasis on the details of the numerical implementation of the method. For the first time, we present the application for a non-Hermitian problem by a numerical example of a one-dimensional atom under the influence of an intense laser field. The efficiency of the method is demonstrated by a comparison with the common Runge–Kutta approach.

Authors:
; ;
Publication Date:
OSTI Identifier:
22701589
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 343; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; LASER RADIATION; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; PROPAGATOR; SCHROEDINGER EQUATION; SOURCE TERMS; TIME DEPENDENCE

Citation Formats

Schaefer, Ido, Tal-Ezer, Hillel, and Kosloff, Ronnie. Semi-global approach for propagation of the time-dependent Schrödinger equation for time-dependent and nonlinear problems. United States: N. p., 2017. Web. doi:10.1016/J.JCP.2017.04.017.
Schaefer, Ido, Tal-Ezer, Hillel, & Kosloff, Ronnie. Semi-global approach for propagation of the time-dependent Schrödinger equation for time-dependent and nonlinear problems. United States. doi:10.1016/J.JCP.2017.04.017.
Schaefer, Ido, Tal-Ezer, Hillel, and Kosloff, Ronnie. Tue . "Semi-global approach for propagation of the time-dependent Schrödinger equation for time-dependent and nonlinear problems". United States. doi:10.1016/J.JCP.2017.04.017.
@article{osti_22701589,
title = {Semi-global approach for propagation of the time-dependent Schrödinger equation for time-dependent and nonlinear problems},
author = {Schaefer, Ido and Tal-Ezer, Hillel and Kosloff, Ronnie},
abstractNote = {A detailed exposition of highly efficient and accurate method for the propagation of the time-dependent Schrödinger equation is presented. The method is readily generalized to solve an arbitrary set of ODE's. The propagation is based on a global approach, in which large time-intervals are treated as a whole, replacing the local considerations of the common propagators. The new method is suitable for various classes of problems, including problems with a time-dependent Hamiltonian, nonlinear problems, non-Hermitian problems and problems with an inhomogeneous source term. In this paper, a thorough presentation of the basic principles of the propagator is given. We give also a special emphasis on the details of the numerical implementation of the method. For the first time, we present the application for a non-Hermitian problem by a numerical example of a one-dimensional atom under the influence of an intense laser field. The efficiency of the method is demonstrated by a comparison with the common Runge–Kutta approach.},
doi = {10.1016/J.JCP.2017.04.017},
journal = {Journal of Computational Physics},
issn = {0021-9991},
number = ,
volume = 343,
place = {United States},
year = {2017},
month = {8}
}